We examine the far-infrared (FIR) properties of a sample of 5391 optically selected QSOs in the 0.5 < z < 2.65 redshift range down to log [νLν, 2500(erg s-1)] > 44.7, using SPIRE data from Herschel-ATLAS. We split the sample in a grid of 74 luminosity-redshift bins and compute the average optical-IR spectral energy distribution (SED) in each bin. By normalizing an intrinsic active galactic nucleus (AGN) template to the AGN optical power (at 5100 Å), we decompose the total IR emission (LIR; 8-1000 µm) into an AGN (LIR, AGN) and star-forming component (LIR, SF). We find that the AGN contribution to LIR increases as a function of AGN power, manifesting as a reduction of the 'FIR bump' in the average QSO SEDs. We note that LIR, SF does not correlate with AGN power; the mean star formation rates (SFRs) of AGN host galaxies are a function of redshift only and they range from ~6 M⊙ yr-1 at z ~ 0 to a plateau of ≲ 200 M⊙ yr-1 at z ~ 2.6. Our results indicate that the accuracy of FIR emission as a proxy for SFR decreases with increasing AGN luminosity. We show that, at any given redshift, observed trends between IR luminosity (whether monochromatic or total) and AGN power (in the optical or X-rays) can be explained by a simple model which is the sum of two components: (i) the IR emission from star formation, uncorrelated with AGN power and (ii) the IR emission from AGN, directly proportional to AGN power in the optical or X-rays.